Re: [Phys-l] pinhole camera

[John Denker <jsd@av8n.com>]

On 04/12/2007 03:54 PM, Michael Porter wrote:

> Could you make the argument that what is formed by a pinhole camera
> isn't really an image (real or not)? There is no coherent
> recombination of light rays in a pinhole camera, just divergence.

That's an interesting question.  I had to think about
that one for a while.

Obviously one "could" make the argument, but as of the
moment I think the opposite approach is better:

The fact is that all images are imperfect.  Real-world
lenses have some inescapable problems (including chromatic
aberration, spherical aberration, and diffraction) and
possibly manufacturing imperfections on top of that.
Furthermore, there are usually depth-of-field issues
in real-world imaging;  devices such as confocal
microscopes /depend/ on controlling depth-of-field.
Also, try analyzing a movie sometime, and observe
how the cameraman uses focus and depth-of-focus to
guide the viewer's attention.

Defining an "image" in terms of a strictly one-to-one
mapping from object points to image points might work
in geometric optics, but it's a non-starter in physical
optics and in real-world applications.

I can't get excited about the fact that a pinhole
camera image is imperfect.

For my money, I call it an image.  I say it is a slightly
out of focus image, with a treeemendous depth of field.

To get a better handle on what I mean by that, consider
the following Gedankenexperiments:
  1) Right in front of the pinhole, install a lens with
   a very long but finite focal length.  That means
   there exists in theory -- geometric optics theory --
   a focal point, just very far away.  The pinhole
   guarantees we have a tremendous depth of field,
   so at the back of our pinhole camera, where we
   expect the image to be, we do in fact find an
   image.  This can be considered the /same/ image
   as formed by the lens, when you take the depth
   of field into account.
  2) Observe that the focal length in item (1) didn't
   actually matter.  So you can take the limit where
   the focal length goes to infinity.  And then you
   can throw away the lens entirely, leaving just a
   plain old pinhole camera.

From this I conclude that the concept of image in a
pinhole camera is either exactly the same as the
conventional concept of image in any other camera, or
at worst the Cauchy principal value of the conventional
concept.  I see no harm in defining (or redefining)
the notion of image to include the pinhole case.


Does anybody have a good counterargument?